Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning

2026-08-31

AI Summary

研究通过跟踪隐藏状态轨迹和分析几何信号来解决多轮对话中语言模型的推理一致性问题，提高任务成功率并降低成本。

Abstract

LLM agents need to sustain goal-consistent reasoning across long multi-turn interactions under strict resource constraints. However, as the multi-turn context accumulates, it can destabilize the underlying LLM's internal representation of task-relevant information from earlier turns, blurring the boundary between constructive reasoning and representation drift. We formulate multi-turn reasoning as a hidden-state trajectory of the underlying LLM that is characterized via two complementary signals: temporal curvature that captures the directional consistency of turn-to-turn updates, and variance slope which measures the expansion or contraction of the exploration space. Across four tasks and three underlying LLMs, we observed that these geometric signals distinguish between correct and incorrect episodes prior to completion. We further decompose each episode into three-action chains formed from four actions (Read, Write, Respond, Transfer) and show that separability is action-dependent, with different signals distinguishing various chain patterns. Our experiments demonstrate that trajectory geometry can identify critical turns in the reasoning process, increasing task success rates on $τ$-Bench from 24.1% to 39.6% while reducing token cost by 11.2%.

Problem

• multi-turn reasoning
• hidden-state trajectory
• representation drift

Innovation

• hidden-state trajectory
• temporal curvature
• variance slope
• multi-turn reasoning